Extended Gaussian mixture regression for forward and inverse analysis

In molecular, material, and process designs, it is important to perform inverse analysis of the regression models constructed with machine learning using target values of the properties and activities. Although many approaches actually employ a pseudo-inverse analysis, Gaussian mixture regression (GMR) can achieve direct inverse analysis. This paper describes the development and use of extended GMR (EGMR), which offers improved predictive ability over conventional GMR. EGMR includes implementations of both GMR and Bayesian GMR, which is based on a variational Bayesian method. The hyperparameters for each model are optimized, and the choice of model for the specific data is determined, through cross-validation. The effectiveness of the proposed EGMR is verified using numerically simulated datasets, compound datasets, a material dataset, and spectral datasets. These datasets contain real data. The predictive ability of EGMR is found to be greater than or equal to that of GMR in all cases, and the prediction errors can be reduced by more than 30%. Furthermore, it is confirmed that EGMR can perform inverse analysis with high reproducibility, even in the extrapolation region of an objective variable. The Python code for EGMR is available at https://github.com/hkaneko1985/dcekit.